The Laws of Thermodynamics and Cyclic Engines

As we have seen, statements of the laws in terms of the conversion of heat into work in a cyclic engine are equivalent to the statements involving energy and entropy. The conversion from one to the other is not always obvious, but the relationships predicting the efficiency of the conversion of heat into work can be derived from the U and S statements. 

Consider as the universe, the cyclic engine plus the two heat reservoirs for which 

Second Law You not only can t get something for nothing, you can t even break 

Still another statement of the second law is the Clausius inequality which states that 

Equation (2.83) modifies equation (2.82) by adding the inequality so that 

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